A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In such a case, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. including part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Conventional lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at once, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
A lithographic apparatus of the type described above may employ a plurality of actuators to position a part of the lithographic apparatus. Examples of parts that may be positioned are the patterning device, the substrate, a part of an irradiation system, a part of an illumination system or any other part of the lithographic apparatus including a metrology frame of the apparatus which is commonly connected to the ground by means of low-frequency air mounts. The air mounts filter vibrations from the ground as much as possible and may include actuators to position the metrology frame with respect to the ground and for instance prevent the metrology frame from drifting.
An example of an actuator for use in lithographic apparatus is described in EP 1.286.222 and US patent publication 2005/0200208, the contents of which are incorporated herein by reference in its entirety. These documents describe a Lorentz actuator including a main magnet system providing a first magnetic field, a subsidiary magnet system providing a second magnetic field, and an electrically conductive element. The main magnet system and the subsidiary magnet system are arranged in Halbach configuration to combine the first and second magnetic field, wherein a magnetization direction of the magnets from the subsidiary magnet system is perpendicular to a magnetization direction of the magnets of the main magnet system. A force can be generated by the interaction between a current carried by the electrically conductive element and the magnetic field.
Motors in general can be characterized by a parameter known as “motor constant”. The motor constant defines a relation between a motor input and a motor output, and in case of a Lorentz actuator the motor input is usually a current carried by the electrically conductive element and the motor output is usually a corresponding generated force due to the current. Most of the time, the motor constant is assumed to be a constant parameter, explaining the name motor constant. However, in practice, motors exhibit a motor position dependent motor constant, which can be divided into a constant average portion and a motor position dependent portion. Thus, when a person skilled in the art assumes a constant motor constant, he/she actually assumes the motor constant to be the constant average portion. The motor constant is motor position dependent due to for instance structural inaccuracies, tolerances, and/or deficiencies or inhomogeneous properties, such as material properties. One of the possible causes for the motor position dependency of the motor constant of a Lorentz actuator can be variations in magnetic field strength and/or magnetization direction/orientation of the magnets.
In this application the motor position is a relative position of different motor parts with respect to each other, e.g. a rotor with respect to a stator. In case of a Lorentz actuator as described above, the motor position is the relative position of the electrically conductive element to the main magnet system.
The motor position dependent portion of the motor constant introduces disturbances in the Lorentz actuator, which negatively influence the position accuracy between the first and second part of the apparatus. This can cause overlay errors and/or imaging problems in the lithographic apparatus.